methods and apparatus to transmit and receive information bits encoded in duobinary, multilevel pulse-amplitude-modulated (PAM) optical signals are described. The transmitted optical signal has a narrow optical spectrum and a low symbol rate. Information bits are encoded in a M-ary PAM symbol sequence, where M≧2. The PAM symbol sequence is input to a finite-state machine, which yields an encoded sequence that changes sign between two symbol intervals when the encoded sequence takes on a nominally zero value during an odd number of intervening symbol intervals. The encoded sequence is lowpass filtered and modulated onto an optical electric field. The receiver processes a received optical electric field to obtain an electrical signal proportional to the received optical intensity, and performs M-ary symbol-by-symbol decisions to recover the transmitted information bits, without potential error propagation.
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7. An optical transmission method, comprising:
encoding representations of data bits into duobinary symbols of first and second duobinary types with a state machine, said first duobinary type having at least three first type values including a particular value and said second duobinary type having at least three second type values including said particular value, wherein the step of encoding includes transitioning from said first duobinary type to said second type for particular said representations of said bits resulting in said particular value for said duobinary symbols; and generating an optical signal having about zero field level for said particular value; having first field levels for said first type values; and having second field levels for said second type values, said second field levels negatives of said first field levels.
1. An optical transmission system, comprising:
a state machine for encoding representations of data bits into a duobinary symbol sequence having first and second duobinary types, said first duobinary type having at least three first type values including a particular value and said second duobinary type having at least three second type values including said particular value, wherein said duobinary symbol sequence makes a transition between said first duobinary type and said second duobinary type for particular said representations of said bits resulting in said particular value; and a modulation subsystem for using said duobinary symbols for generating an optical signal having about zero field level for said particular value; having first field levels for said first type values; and having second field levels for said second type values, said second field levels negatives of said first field levels.
2. The system of
said duobinary symbol sequence takes on said particular value for particular said representations of said bits and takes on another value different than said particular value for all other said representations of said bits.
3. The system of
the state machine includes a subsequence decomposer for generating a subsequence logic sequence having a first subsequence logic level for particular said representations of said bits resulting in said particular value for said duobinary symbols and a second subsequence logic level for all other said representations of said bits; and a precoder for generating precode logic sequence switching between a first precode logic level and a second precode logic level for said first subsequence logic level and not switching between said first and second precode logic levels for said second subsequence logic level, said first precode logic level used for generating said duobinary symbols of one of said first and second duobinary types and said second precode logic level used for generating said duobinary symbols of the other of said first and second duobinary types.
4. The system of
said precoder includes a delay element for delaying said precode logic sequence and a comparator for comparing said delayed precode logic sequence with said subsequence logic sequence for providing said precode logic sequence.
5. The system of
the state machine further includes a selective inverter for inverting a value representation of said bits for said first precode logic level for providing one of said first and second duobinary type values and not inverting said value representation of said bits for said second precode logic level for providing the other of said first and second duobinary type values.
6. The system of
the modulation subsystem includes a phase modulator for providing one of said first and second field levels for said first precode logic level and providing the other of said first and second field levels for said second precode logic level.
8. The method of
the step of encoding includes taking on said particular value for particular said representations of said bits and taking on another value different than said particular value for all other said representations of said bits.
9. The method of
the step of encoding comprises generating a subsequence logic sequence having a first subsequence logic level for particular said representations of said bits resulting in said particular value for said duobinary symbols and a second subsequence logic level for all other said representations of said bits; switching between a first precode logic level and a second precode logic level for said first subsequence logic level and not switching between said first and second precode logic levels for said second subsequence logic level; and using said first precode logic level for generating one of said first and second duobinary types and using said second precode logic level for generating the other of said first and second duobinary types.
10. The method of
the step of preceding further comprises delaying said precode logic sequence; and comparing said delayed precode logic sequence with said subsequence logic sequence for providing said precode logic sequence.
11. The method of
the step of encoding further comprises inverting a value representation of said bits for said first precode logic level for providing one of said first and second duobinary type values and not inverting said value representation of said bits for said second precode logic level for providing the other of said first and second duobinary type values.
12. The method of
the step of generating said optical signal further comprises phase modulating said optical signal for providing one of said first and second field levels for said first precode logic level and providing the other of said first and second field levels for said second precode logic level.
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This application is a continuation of application Ser. No. 09/774,288 filed Jan. 29, 2001 by the same inventors and assigned to the same assignee now U.S. Pat. No. 6,424,444.
1. Field of the Invention
The invention relates generally to optical communication systems and, more particularly, to transmission and reception of digital information bits encoded in duobinary, multilevel pulse-amplitude modulation optical signals which, for a given bit rate, have a narrow optical spectrum and low symbol rate, and enable the information bits to be recovered from the intensity of the received optical signal without potential error propagation.
2. Description of the Prior Art
It is well known that in optical communication systems conveying digital information, whether they transmit a single signal at a single carrier wavelength or transmit multiple signals at different carrier wavelengths (i.e., employ wavelength-division multiplexing), for a fixed bit rate per carrier wavelength, it is beneficial to design the transmitted signal to have a narrow optical spectrum and to use a long symbol interval. Throughout this patent, the term "optical spectrum" refers to the power spectral density of the transmitted optical electric field.
Furthermore, implementation of optical communication systems is simplified greatly if the transmitted signal is designed so that the transmitted information bits can be recovered at the receiver simply by extracting from the received optical signal an electrical signal proportional to the intensity of the received optical signal (i.e., the absolute square of the received optical electric field), and performing symbol-by-symbol decisions. Currently, almost all practical optical communication systems use direct detection, in which a photodetector generates a photocurrent proportional to the received optical signal intensity. It is also possible to extract an electrical signal proportional to the received optical signal intensity through other means, e.g., asynchronous homodyne or asynchronous heterodyne detection.
Single-sideband amplitude modulation is a traditional means to narrow the spectrum of a modulated signal by a factor of two, and involves modulation of a signal and its Hilbert transform onto quadrature carriers at the same carrier frequency. A few prior works have described single-sideband modulation of optical signals, but the single-sideband optical modulation schemes proposed to date are very difficult to implement in practice. Vestigial-sideband amplitude modulation is essentially an imperfect practical implementation of single-sideband amplitude modulation. Optical vestigial-sideband amplitude modulation can be implemented by first generating an amplitude-modulated optical signal and then filtering it with an optical filter having a sharp cutoff centered at the optical carrier frequency but, in practice, it is difficult to fabricate filters having sufficiently sharp cutoff and to match the optical carrier frequency and filter cutoff frequency with sufficient accuracy.
Multiple-subcarrier modulation (also called subcarrier multiplexing) represents a well-known approach to increasing the symbol interval. In this approach, the information bit stream is divided into multiple substreams at lower bit rates, and each substream is modulated onto an electrical subcarrier at a different subcarrier frequency. The modulated subcarriers are summed to form a frequency-division-multiplexed electrical signal, which is then modulated onto an optical carrier, usually by intensity modulation. While multiple-subcarrier modulation lengthens the interval of symbols transmitted on individual subcarriers, it does not necessarily reduce the total optical bandwidth of the transmitted signal. Multiple-subcarrier modulation offers poor average optical-power efficiency (e.g., compared to on-off keying, which is the same as 2-ary pulse-amplitude modulation), and this efficiency decreases further as the number of subcarriers is increased. Multiple-subcarrier modulation requires transmitters and receivers significantly more complicated than those required by baseband modulation techniques, such as on-off keying and M-ary pulse-amplitude modulation.
Modulation of information bits onto optical signals using M-ary phase-shift keying (for M≧3) or using M-ary quadrature-amplitude modulation (for M≧4) represent other well-known means to narrow the optical spectrum and lengthen the symbol interval of the transmitted signal. However, very complicated phase-sensitive detection techniques are required to recover the transmitted bits, such as synchronous homodyne or synchronous heterodyne detection.
It is well-known that M-ary pulse-amplitude modulation, in which information bits are encoded in one of M intensity levels during each symbol interval, where M≧3, represents a means to narrow the optical spectrum and lengthen the symbol interval as compared to on-off keying (which is equivalent to 2-ary pulse-amplitude modulation). It is well-known that for a given information bit rate, as M is increased, the spectrum narrows and the symbol interval increases. A key drawback of M-ary pulse-amplitude modulation is that for a given M, it does not offer the maximal spectral narrowing that can be achieved.
M-ary pulse-amplitude modulation with duobinary encoding is a well-known modulation technique that has been widely studied for a variety of communication media. For reasons to be described below, to date, only M=2 has been chosen in optical communication systems. In this technique, a sequence of M-ary pulse-amplitude modulation symbols, Im, where m is a time index of symbol intervals, is encoded to yield a duobinary symbol sequence Bm=Im+Im-1, which is transmitted. Duobinary encoding narrows the spectrum of the transmitted signal, and choosing M>2 provides additional spectral narrowing and lengthens the symbol interval. A duobinary M-ary pulse-amplitude modulation signal takes on 2M-1 possible levels, including M-1 negative levels, M-1 positive levels, and zero. Optimal detection of duobinary M-ary pulse-amplitude modulation signals requires maximum-likelihood sequence detection, but at high bit rates, this is difficult to implement, so that symbol-by-symbol detection is typically performed, and the symbol sequence Im is precoded to avoid error propagation in the recovered information bits.
Numerous patents and research papers have documented the use of 2-ary pulse-amplitude modulation (which is equivalent to on-off keying) with duobinary encoding in optical communication systems. To our knowledge, all of these works have utilized preceding to permit symbol-by-symbol detection without error propagation. While these works have described many different techniques to implement precoding, duobinary encoding and modulation of the duobinary signal onto the optical carrier, all of these techniques result in transmission of equivalent optical signals, which take on one of three possible electric-field amplitude values, e.g., {-a, 0, a}. Using precoded, 2-ary pulse-amplitude modulation with duobinary encoding, it is possible to recover the transmitted information bits by performing symbol-by-symbol detection on a signal proportional to the received optical intensity, such as the photocurrent in a direct-detection receiver. 2-ary pulse-amplitude modulation with duobinary encoding offers essentially the same average optical-power efficiency as on-off keying. While this technique narrows the optical spectrum by about a factor of two (as compared to on-off keying), it does not provide the narrowing that would be possible for M>2, nor does it lengthen the symbol interval (as compared to on-off keying).
It is highly desirable to employ duobinary M-ary pulse-amplitude modulation, M>2, in optical communication systems, to achieve both a narrower optical spectrum and a longer symbol interval. However, with all previously known precoding techniques, it is not possible to recover the transmitted information bits using symbol-by-symbol detection on a signal proportional to the received optical intensity, such as the photocurrent in a direct-detection receiver, without potential error propagation. Using all previously known preceding techniques, for M>2, it would be necessary to employ a complicated, phase-sensitive detection technique to receive the optical signal, e.g., synchronous homodyne or synchronous heterodyne detection. Hence, to date, it has not been possible to use duobinary M-ary pulse-amplitude modulation, for M>2, in practical optical communication systems using direct-detection receivers.
There is a need for methods and apparatus to transmit and receive duobinary M-ary pulse-amplitude-modulated signals in optical communication systems, for any choice of M>2, and for any choice of the M intensity levels, where the signals are precoded such that the transmitted information bits can be recovered using symbol-by-symbol detection on a signal proportional to the received optical intensity, e.g., by using a simple direct-detection receiver, without potential error propagation.
It is therefore an object of the present invention to provide methods and apparatus to transmit and receive duobinary M-ary pulse-amplitude-modulated optical signals, for M>2, in optical communication systems.
Another object is to provide methods and apparatus to precode duobinary M-ary pulse-amplitude-modulated optical signals, for M>2, such that the transmitted information bits can be recovered using symbol-by-symbol detection on a signal proportional to the received optical intensity, e.g., by using a simple direct-detection receiver, without the potential for error propagation.
Briefly, in a preferred embodiment of a duobinary M-ary pulse-amplitude modulation optical transmission system, information bits to be transmitted are formed into blocks of k bits, where k≦log2M. Blocks of k bits are input to a M-ary pulse-amplitude modulation symbol encoder, which encodes each block into a pulse-amplitude modulation symbol taking on one of M levels D(0), . . . , D(M-1), where M≧2. The level D(0) is nominally zero, and the remaining M-1 levels, D(1), . . . , D(M-1), are nonzero and all of the same sign. This encoding is performed using Gray coding. The encoder output is a M-ary pulse-amplitude modulation symbol sequence Dm, where m is a time index counting symbol intervals. When M>2, for a given information bit rate, the duration of each symbol interval is longer than the symbol interval using 2ary pulse-amplitude modulation (which is equivalent to on-off keying).
The M-ary pulse-amplitude modulation symbol sequence Dm is input to a finite-state machine, which effectively performs two functions. The finite-state machine effectively precodes the symbol sequence so that at the receiver, the transmitted information bits can be recovered from the received optical signal using symbol-by-symbol detection on a signal proportional to the received optical intensity, e.g., by using a simple direct-detection receiver, without the potential for error propagation. At the same time, the finite-state machine effectively performs duobinary encoding, which introduces temporal correlation in the symbol sequence for the purpose of narrowing the spectrum of the transmitted optical signal by approximately a factor of two as compared to a M-ary pulse-amplitude modulation signal that has not been duobinary encoded.
Within the finite-state machine, the M-ary pulse-amplitude modulation symbol sequence Dm is input to a subsequence decomposer, which forms a logical subsequence Sm,0, which is a binary sequence having symbol interval T, and is associated with the level D(0). During each symbol interval, the logical subsequence Sm,0 takes on a logical 0 unless the sequence Dm takes on the level D(0), in which case, the logical subsequence Sm,0 takes on a logical 1.
The logical subsequence Sm,o is input to a logical subsequence precoder, which includes an exclusive-OR gate and a one-symbol delay interconnected in a feedback arrangement. The output of the logical subsequence precoder is the logical precoded subsequence Zm, which is related to Sm,0 by Zm=Sm,0-Zm-l (mod2). The pulse-amplitude modulation symbol sequence Dm and the logical precoded subsequence Zm are input to a selective inverter, which yields the duobinary precoded pulse-amplitude modulation symbol sequence Bm. During each symbol interval, Bm=Dm if Zm takes on a logical 1, and Bm=-Dm if Zm takes on a logical 0.
During each symbol interval, the sequence Bm takes on one of a set of 2M-1 levels, which include the nominally zero level D(0), the M-1 positive levels D(1), . . . , D(M-1), and the M-1 negative levels -D(1), . . . , -D(M-1). The sequence Bm takes on nonzero levels of opposite signs during two distinct symbol intervals if and only if the sequence Bm takes on the nominally zero level D(0) during an odd number of symbol intervals between these two symbol intervals. The sequence Bm is lowpass filtered, resulting in the duobinary precoded pulse-amplitude modulation signal s(t). Like the sequence Bm, the signal s(t) takes on a set of 2M-1 levels, including one nominally zero level, M-1 positive levels, and M-1 negative levels which are, respectively, the negatives of the M-1 positive levels. Moreover, like Bm, s(t) changes sign between two symbol intervals if and only if it takes on a nominally zero value during an odd number of intervening symbol intervals.
The duobinary precoded pulse-amplitude modulation signal s(t) is then modulated onto an optical carrier using a modulation subsystem. In the modulation subsystem, a laser or other light source generates an unmodulated optical carrier, which is input to a dual-drive, push-pull, Mach-Zehnder interferometric intensity modulator. The intensity modulator is driven by complementary drive signals V1(t)=Gs(t) and V2(t)=-Gs(t), each of which takes on values between -Vπ/2 and Vπ/2, where Vπ is the drive voltage required to produce a phase shift of π. The intensity modulator is biased by a d.c. bias chosen so that the modulator output is approximately zero when the drive signals V1(t) and V2(t) are zero. The modulator output is a duobinary M-ary pulse-amplitude-modulated optical signal described by the transmitted optical electric field Etrans(t). Like the sequence Bm and the signal s(t), Etrans(t) takes on a set of 2M-1 levels, including one nominally zero level, M-1 positive levels, and M-1 negative levels which are, respectively, the negatives of the M-1 positive levels. Moreover, like Bm and s(t), Etrans(t) changes sign between two symbol intervals if and only if it takes on a nominally zero value during an odd number of intervening symbol intervals. The transmitted optical electric field Etrans(t) is launched into the optical transmission medium, which may be a fiber or free-space optical medium.
At the output of the optical transmission medium, the received duobinary M-ary pulse-amplitude-modulated optical signal is described by the received optical electric field Erec(t). The transmitted information bits can be recovered from the received optical electric field Erec(t) using a direct-detection receiver, an asynchronous homodyne receiver, or an asynchronous heterodyne receiver. While each of these three receiver designs is implemented differently, each extracts from the received optical electric field Erec(t) a M-ary pulse-amplitude modulation signal v(t), which depends on Erec(t) only through the received optical intensity Irec(t)=|Erec(t)|2. Accordingly, the M-ary pulse-amplitude modulation signal v(t) takes on M-1 positive levels and one level that is approximately zero. The M-ary pulse-amplitude modulation signal v(t) is input to a M-ary pulse-amplitude modulation decision device, which performs M-ary symbol-by-symbol decisions by comparing the M-ary pulse-amplitude modulation signal v(t) to a set of M-1 thresholds. Because the M-ary pulse-amplitude modulation decision device does not perform decisions by comparing values of the M-level pulse-amplitude modulation signal v(t) in successive symbol intervals, decisions are not subject to error propagation. The M-ary pulse-amplitude modulation decision device yields at its output blocks of k recovered information bits, which are converted to a serial sequence of recovered information bits by a parallel-to-serial converter.
An advantage of the present invention is that the transmitted optical signal has a narrow optical spectrum, so that in wavelength-division-multiplexed systems, which utilize some form of optical or electrical filters to select the desired signal at the receiver, the spacing between carrier frequencies can be reduced subject to some constraints on the tolerable distortion to the desired signal caused by these filters and the tolerable crosstalk from undesired signals not rejected by these filters, thereby increasing the spectral efficiency of the system.
Another advantage of the present invention is that the transmitted optical signal has a narrow optical spectrum, reducing pulse spreading caused by chromatic dispersion in systems using single-mode fiber as the transmission medium.
Another advantage of the present invention is that the transmitted optical signal has a long symbol interval, improving the receiver's ability to recover the transmitted information bits in the presence of dispersion (i.e., pulse spreading) originating from several sources, including chromatic dispersion or polarization-mode dispersion in single-mode fiber, modal dispersion in multi-mode fiber, and multipath propagation in free-space links.
Another advantage of the present invention is that the transmitted optical signal has a long symbol interval, reducing the electrical bandwidth required of electrical-to-optical converters, optical-to-electrical converters and electrical components in the transmitter and receiver.
Another advantage of the present invention is that the transmitted optical signal has a long symbol interval, reducing the clock speed required in the transmitter and receiver.
Another advantage of the present invention is that the transmitted information bits can be recovered using symbol-by-symbol detection on a signal proportional to the received optical intensity, such as the photocurrent in a direct-detection receiver.
These and other objects and advantages of the present invention will no doubt become obvious to those of ordinary skill in the art after having read the following detailed description of the preferred embodiments, which are illustrated in the various figures.
We can describe the duobinary precoded pulse-amplitude modulation symbol sequence as follows. During each symbol interval, this sequence takes on one of a set of 2M-1 levels. This set of levels includes one level that is nominally zero, M-1 positive levels and M-1 negative levels which are, respectively, approximately the negatives of the positive levels. The duobinary precoded pulse-amplitude modulation symbol sequence takes on nonzero levels of opposite signs during two distinct symbol intervals if and only if this sequence takes on the nominally zero level during an odd number of symbol intervals between these two symbol intervals.
The duobinary precoded pulse-amplitude modulation symbol sequence is fed into a lowpass filter, which further narrows the spectrum of the duobinary precoded pulse-amplitude modulation symbol sequence, yielding the duobinary precoded pulse-amplitude modulation signal. Note that although it represents a lowpass-filtered version of the duobinary precoded pulse-amplitude modulation symbol sequence, the duobinary precoded pulse-amplitude modulation signal also conforms to the description given in the previous paragraph. In particular, the duobinary precoded pulse-amplitude modulation signal takes on a set of 2M-1 levels, and it changes sign from one symbol interval to another if and only if it takes on a nominally zero level during an odd number of intervening symbol intervals.
While all of the embodiments of the invention described here explicitly describe the use of one or more lowpass filter(s), it should be emphasized that this(these) filter(s) may be implicitly included in one or more elements of the transmitter. The output of 24 comprises one or more encoded pulse-amplitude modulation signal(s) 25 that convey the duobinary precoded pulse-amplitude modulation signal.
Throughout this patent, we will describe optical signals in terms of their electric fields and their intensities (i.e., instantaneous powers). To define our notation, we consider an abstract optical signal X. In reality, the electric field of X is a real, passband signal at an optical carrier frequency ωo. We denote this real, passband electric field by EX,rp(t):
where φo is the real optical carrier phase, and where EX(t) and φX(t) are the real, non-negative magnitude and the real phase of the optical signal X, respectively. We will find it convenient to represent the optical signal X by a complex, baseband electric field EX,cb(t):
Note that the complex, baseband electric field EX,cb(t) completely describes the modulation impressed on the signal X(in the form of EX(t) and φX(t)), but does not describe the carrier frequency ωo, nor the carrier phase φo. Given EX,cb(t), the carrier frequency ωo, and the carrier phase φo, we can recover EX,rp(t) as follows:
In this patent, we will frequently consider an optical signal X such that EX,cb(t) takes on real values that are zero, positive or negative. Note that when EX,cb(t) is positive, then φX(t)=0 (alternatively, we can say that φX(t) is equal to any even integral multiple of π). When EX,cb(t) is negative, then φX(t)=π (alternatively, we can say that φX(t) is equal to any odd integral multiple of π, such as -π). Given EX,cb(t), we can compute the intensity of the optical signal X:
Hereafter in this patent, we will always refer to the electric field of an optical signal X in terms of the complex, baseband electric field EX,cb(t), and we will omit the subscript "cb".
The encoded pulse-amplitude modulation signal(s) 25 are input to a modulation subsystem 26, which modulates 25 onto an optical carrier electric field. The modulation subsystem 26 includes an optical signal generator 27. Within 27, a laser or other light source 28 generates an optical carrier described by an optical carrier electric field Ecarrier(t), denoted by 29. The optical carrier electric field 29 is passed into one or more modulator(s) 30, which are biased by one or more suitable d.c. bias signals 31. Within 26, the encoded pulse-amplitude modulation signal(s) 25 is(are) passed to a signal generator driver 32, which may include one or more element(s) to process the signal(s) 25, as well as one or more driver(s) to generate drive signal(s) 33. The drive signal(s) 33 is(are) passed into the optical signal generator 27 for driving the modulator(s) 30. In some embodiments, 33 also drives the light source 28. The encoded pulse-amplitude modulation signal(s) 25 are thereby modulated onto the optical carrier electric field 29, yielding a transmitted optical electric field Etrans(t), denoted by 34.
The transmitted optical electric field 34 can be described as a duobinary M-ary pulse-amplitude-modulated optical signal, which can be described in terms of a sequence of encoded symbols, each having interval T. In the present invention, the symbol interval T is longer than the symbol interval in systems using 2-ary pulse-amplitude modulation or duobinary 2-ary pulse-amplitude modulation by a factor log2M, assuming M=2k. For example, when M=4, the symbol interval is lengthened by a factor of 2.
During a given symbol interval, the transmitted optical electric field 34 takes on one of a set of 2M-1 levels, which we denote as {E(i), i=-(M-1), . . . ,0, . . . ,M-1}. This set of levels includes one level that is nominally zero, E(0)≡0, which may be nonzero in practice because of a finite extinction ratio in the optical modulator(s), and/or because of imperfections in the modulator d.c. bias 31 and/or the drive signal(s) 33. The set of levels taken on by the transmitted optical electric field 34 includes a set of M-1 positive levels {E(i)>0, i=1, . . . , M-1}, and a set of M-1 negative levels {E(i)≡-E(-i)<0, =-(M-1), . . . , -1} which are, respectively, approximately the negatives of the positive levels. We recall that the transmitted optical intensity Itrans(t) is given by the absolute square of the transmitted optical electric field 34, i.e., Itrans(t)=|Etrans(t)|2. Hence, during a given symbol interval, the transmitted optical intensity Itrans(t) takes on one of a set of M non-negative levels, which we denote as {I(i), i=0, . . . , M-1l},where one of the levels is nominally zero I(0)=|E(0)|2≡0, and where the remaining non-zero levels are given by I(i)=|E(i)|2>0, i=1, . . . , M-1. For example, if the transmitted optical electric field 3 takes on the levels {-{square root over (3)},-{square root over (2)},-1,0,1,{square root over (2)},{square root over (3)}}, then the transmitted optical intensity Itrans(t) takes on the levels {0, 1, 2, 3}. The temporal properties of the transmitted optical electric field 34, which are key to narrowing the optical spectrum of 34, can be described as follows. The transmitted optical electric field 34 takes on nonzero levels of opposite signs during two distinct symbol intervals if and only if 34 takes on the nominally zero level E(0) during an odd number of symbol intervals between these two symbol intervals.
A sequence of levels of the transmitted electric field 34 under the present invention can be described in terms of a sequence of transitions of a finite-state machine. A state-transition diagram for such finite-state machine is shown in
In order to describe mathematically how the transitions of the finite-state machine govern the sequence of transmitted electric field levels, we define Etrans,m to be the value of the transmitted optical electric field Etrans(t) (34) at symbol interval m. Similarly, we define Itrans,m=|Etrans,m|2 to be the value of the transmitted optical intensity Itrans(t)=|Etrans(t)|2 at symbol interval m. The state-transition diagram 37 has four possible transitions 39a, 39b, 39c and 39d, which are indicated by arcs. Each state transition 39a, 39b, 39c and 39d proceeds in the direction indicated by the arrow. For a transition occurring at symbol interval m, the starting state is the result of a transition that occurred at symbol interval m-1, and this starting state governs Etrans,m, the electric field level transmitted at symbol interval m. For a transition occurring at symbol interval m, the ending state is the result of the transition occurring at symbol interval m, and this ending state will govern Etrans,m+1, the electric field level transmitted at symbol interval m+1. Each of the transitions 39a, 39b, 39c and 39d is labeled by the corresponding values of Etrans,m and Itrans,m (we follow a convention common in state-transition diagrams and separate these values by a "/" symbol).
The transition 39a has starting state X-(38a) and ending state X-(38a); at symbol interval m, the information bits are to be encoded in one of the M-1 positive intensity levels Itrans,m=I(i), iε{1, . . . , M-1}, and the transmitted electric field takes on the specific negative level whose absolute square equals Itrans,m, i.e., Etrans,m=-E(i), i∈{1, . . . ,M-1}. Note that for transition 39a, the starting and ending states are identical because Itrans,m is nonzero (i.e., Etrans,m is nonzero). Similarly, the transition 39b has starting state X+(38b) and ending state X+(38b); at symbol interval m, the information bits are to be encoded in one of the M-1 positive intensity levels Itrans,m=I(i), iε{1, . . . , M-1}, and the transmitted electric field takes on the specific positive level whose absolute square equals Itrans,m, i.e., Etrans,m=E(i), iε{1, . . . , M-1}. The transition 39c has starting state X-(38a) and ending state X+(38b); at symbol interval m, the information bits are to be encoded in the nominally zero intensity level I(0)≡0, and the transmitted electric field takes on the nominally zero level E(0)≡0. Note that for transition 39c, the starting and ending states are distinct because Itrans,m is zero (i.e., Etrans,m is zero). Similarly, the transition 39d has starting state X+ (38b) and ending state X-(38a); at symbol interval m, the information bits are to be encoded in the nominally zero intensity level I(0)≡0, and the transmitted electric field takes on the nominally zero level E(0)≡0.
The finite-state machine described by the state-transition diagram 37 is the simplest finite-state machine capable of describing the sequence of transmitted electric field levels under the present invention, in that this finite-state machine has the minimum required number of states, which is two. Since the finite-state machine described by 37 has only two states, the storage of only a single bit is required to keep track of the state, which facilitates implementation. Nonetheless, it is possible to describe the sequence of transmitted electric field levels using another finite-state machine having more than two states. In order to describe correctly a sequence of transmitted electric field levels under the present invention, a finite-state machine must have at least two types of states. The finite-state machine must make a transition from a state of one of these two types to a state of the other of these two types for each symbol interval in which the transmitted electric field takes on the zero level. Moreover if the finite-state machine is in a state of one of these two types, the transmitted electric field level should be either zero or positive; if the finite-state machine is in a state of the other of these two types, the transmitted electric field level should be either zero or negative.
Our description of a sequence of transmitted electric field levels in terms of a sequence of transitions of the finite-state machine is equivalent to the description of the sequence of transmitted field levels given previously, i.e., that the transmitted optical electric field 34 takes on nonzero levels of opposite signs during two distinct symbol intervals if and only if 34 takes on the nominally zero level E(0) during an odd number of symbol intervals between these two symbol intervals.
The optical spectrum of the transmitted optical electric field 34 depends on the design of the symbol encoder, the lowpass filter, and other elements within 24. The optical spectrum also depends on the design of the modulation subsystem 26. Accordingly, the optical spectrum is different for the various embodiments of the invention described below. Nonetheless, for all of the embodiments of duobinary M-ary pulse-amplitude modulation following the present invention, the optical spectrum is narrowed by a factor of approximately 2 as compared to M-ary pulse-amplitude modulation, by a factor of approximately log2M as compared to duobinary 2-ary pulse-amplitude modulation, and by a factor of approximately 2log2M as compared to 2-ary pulse-amplitude modulation (on-off keying).
The transmitted optical electric field 34 is launched into the optical transmission medium 19, which may be a fiber or free-space optical medium. In the former case, the optical transmission medium may include single- and/or multi-mode fiber, one or more optical amplifier(s), one or more optical multiplexer(s) and/or demultiplexer(s), and one or more optical filter(s). If present, some of these optical components, such as multiplexers or filters, may serve to further narrow the optical spectrum of the transmitted optical signal. At the output of the optical transmission medium 19, the received duobinary M-ary pulse-amplitude-modulated optical signal is a received optical electric field Erec(t), denoted by 36. We recall that the received optical intensity is given by Irec(t)=|Erec(t)|2.
denoted by 55 and 56, respectively, and quadrature linear combinations
denoted by 57 and 58, respectively. In a practical implementation, an asynchronous homodyne receiver typically includes some means to match the polarizations of the received optical electric field 36 and the local oscillator optical electric field 53, but this polarization-matching means is omitted from
denoted by 91 and 92, respectively. In a practical implementation, an asynchronous heterodyne receiver typically includes some means to match the polarizations of the received optical electric field 36 and the local oscillator optical electric field 87, but this polarization-matching means is omitted from
As we have seen, each of the three receiver embodiments 20a, 20b and 20c, extracts from the received optical electric field 36 the M-level pulse-amplitude modulation signal 43 that is proportional to the received optical intensity Irec(t)=|Erec(t)|2. In other words, the M-level pulse-amplitude modulation signal 43 is essentially equivalent in each of the three receiver embodiments 20a, 20b and 20c. Having extracted the M-level pulse-amplitude modulation signal 43, each of the three receiver embodiments 20a, 20b and 20c acts in an identical fashion to perform performs symbol-by-symbol M-ary decisions to yield the recovered information bits 50, without the potential for error propagation.
We will now describe in detail various embodiments of the duobinary M-ary pulse-amplitude modulation transmitter 18, including various embodiments of 24 and various embodiments of 26. For these various embodiments of 18, we will describe the transmitted optical electric field 34, the received optical electric field 36 and the M-level pulse-amplitude modulation signal 43; and we will describe how the M-ary pulse-amplitude modulation decision device 44 can make symbol-by-symbol M-ary decisions to obtain the recovered information bits 50 without potential error propagation.
The sequence 231 is input to a finite-state machine, denoted by 232. In some embodiments of 229, the block of k information bits (23) is also input to the finite-state machine 232, as indicated in 229. In some cases, having direct access to the information bits 23 may simplify the implementation of the finite state machine 232. The finite-state machine 232 performs two functions simultaneously. The finite-state machine 232 effectively precodes the symbol sequence so that at the receiver, the transmitted information bits can be recovered from the received optical signal using symbol-by-symbol detection on a signal proportional to the received optical intensity, e.g., by using a simple direct-detection receiver, without the potential for error propagation. At the same time, the finite state machine 232 effectively performs duobinary encoding, which introduces temporal correlation in the symbol sequence for the purpose of narrowing its spectrum. The finite state machine 232 issues the duobinary precoded pulse-amplitude modulation symbol sequence Bm, denoted by 233.
We can describe the sequence Bm (233) as follows. During each symbol interval the sequence 233 takes on one of a set of 2M-1 levels {D(i), i=-(M-1), . . . , 0 M-1}. This set of levels includes the nominally zero level D(0), the set of M-1 positive levels {D(i)>0, i=1, . . . , M-1}, and the set of M-1 negative levels {D(i)≡-D(-i )<0, i=-(M-1), . . . , -1}, which are, respectively, the negatives of the positive levels. The sequence 233 takes on nonzero levels of opposite signs during two distinct symbol intervals if and only if the sequence 233 takes on the nominally zero level D(0) during an odd number of symbol intervals between these two symbol intervals.
The above description of the sequence Bm (233) is analogous to the description of the sequence of levels of the transmitted optical electric field (34), i.e., that 34 takes on nonzero levels of opposite signs during two distinct symbol intervals if and only if 34 takes on the nominally zero level E(0) during an odd number of symbol intervals between these two symbol intervals. Therefore, the finite-state machine 232, which governs the sequence 233, is analogous to the finite-state machine governing 34. The finite-state machine 232 can be described in terms of a state-transition diagram shown in
The state-transition diagram 234 has four possible transitions 234c, 234d, 234e and 234f, which are indicated by arcs. Each of the transitions 234c, 234d, 234e and 234f is labeled by the corresponding values of Dm (231) and Bm (233). (In the state-transition diagram 234, we have also labeled the states 234a and 234b by corresponding values of Zm-1 (243,
The finite-state machine 232, which is described by the state-transition diagram 234, is the simplest finite-state machine capable of governing the sequence 233, in that 232 has the minimum required number of states, which is two. It is also possible to govern the sequence 233 using a finite-state machine having more than two states, although this would complicate implementation of the finite-state machine. In order to govern the sequence 233, a finite-state machine must have at least two types of states. The finite-state machine must make a transition from a state of one of these two types to a state of the other of these two types for each symbol interval at which the sequence 233 on the zero level. Moreover if the finite-state machine is in a state of one of these two types, Bm (233) should be either zero or positive; if the finite-state machine is in a state of the other of these two types, Bm (233) should be either zero or negative.
The sequence 233 passes into a lowpass filter 235, whose output is a duobinary precoded pulse-amplitude modulation signal s(t), denoted by 236. Note that 236 corresponds to 25 in FIG. 2. Since the lowpass filter 235 is a linear system, the levels taken on by the signal 236 are proportional to the levels taken on by the sequence 233. Accordingly, the signal 236 conforms to the description of the sequence 233 given above. Specifically, the signal 236 takes on a set of 2M-1 levels, and the signal 236 takes on nonzero levels of opposite sign during two distinct symbol intervals if and only if the signal 236 takes on the nominally zero level during an odd number of symbol intervals between these two symbol intervals. Although in the embodiment 229 we show the lowpass filter 235 as a separate component, the lowpass filter may not be present as a separate component, and the lowpass filtering function may be performed by one or more other components in the duobinary M-ary pulse-amplitude modulation signal encoder or in the modulation subsystem that follows it.
In practice, the choice of the M levels that are to be taken on by the sequence 231, which determines the 2M-1 levels taken on by the sequence 233 and the signal 236, depends on the characteristics of the modulation subsystem 26 used to modulate the signal 236 onto the optical carrier electric field 29 to produce the transmitted optical electric field 34, and also depends on the set of levels that are to be taken on by the transmitted optical electric field 34, and thus the transmitted optical intensity Itrans(t). We will provide a detailed example after we have described the transfer characteristics of typical embodiments of the modulation subsystem 26.
In the encoder 229a, the sequence 231 enters the finite-state machine 232a, within which 231 is input to a subsequence decomposer 237, which forms the logical subsequence Sm,0, denoted by 238. The subsequence 238 is a binary sequence having symbol interval T, and is associated with the level D(0). During each symbol interval, the logical subsequence 238 takes on a logical 0 unless the sequence 231 takes on the level D(0), in which case, the logical subsequence 238 takes on a logical 1. Mathematically, during the mth symbol interval, Sm,0=0 if Dm≠D(0) and Sm,0=1 if Dm=D(0).
The logical subsequence 238 is input to a logical subsequence precoder, which is denoted by 239. The precoder 239 includes an exclusive-OR gate (modulo-2 subtractor), denoted by 240, as well as a one-symbol delay, denoted by 241, interconnected in a feedback arrangement. The output of the logical subsequence precoder 239 is a logical precoded subsequence Zm, denoted by 242. The logical precoded subsequence 242 is related to the logical subsequence 238 by the rule that, during the mth symbol interval, Zm=Sm,0-Zm-1 (mod2), where Zm-1 (243) is the value of the logical precoded subsequence Zm (242) during the previous symbol interval, m-1. We note that the precoder 239 is itself a finite-state machine with input Sm,0 (238), output Zm (242), and two states, corresponding to the two possible values of Zm-1 (243). The operation of 239 is described by the state-transition diagram 234, shown in
Within the encoder 229a, the pulse-amplitude modulation symbol sequence Dm, denoted by 231, and the logical precoded subsequence Zm, denoted by 242, are input to a selective inverter 244, which yields the duobinary precoded pulse-amplitude modulation symbol sequence Bm, denoted by 233. During each symbol interval, Bm=Dm if Zm takes on a logical 1, and Bm=-Dm if Zm takes on a logical 0. We observe that since the sequence Dm (231) takes on non-negative levels, the sequence Dm (231) is the magnitude of the sequence Bm (233) and the sequence Zm (242) provides a logical indication of the sign of the sequence Bm (233). These observations will help explain the design of an alternate embodiment of the encoder, which is described below. In the encoder 229a, the sequence Bm (233) is input to the lowpass filter 235, whose output is the signal s(t) (236). Although in the embodiment of the encoder 229a we show the lowpass filter 235 as a separate component, the lowpass filter may not be present as a separate component, and the lowpass filtering function may be performed by one or more other components in the duobinary M-ary pulse-amplitude modulation signal encoder or in the modulation subsystem that follows it.
We now provide an example of a specific embodiment of the duobinary M-ary pulse-amplitude modulation signal encoder 229 for the specific case of M=4, assuming a specific mapping between information bits and 4-ary pulse-amplitude modulation symbols. This embodiment of a duobinary 4-ary pulse-amplitude modulation signal encoder is shown in
TABLE 1 | ||||
X1 | X2 | Dm | Sm,0 | |
0 | 0 | D(0) = 0.00 | 1 | |
0 | 1 | D(1) = 1.18 | 0 | |
1 | 1 | D(2) = 1.82 | 0 | |
1 | 0 | D(3) = 3.00 | 0 | |
In the encoder 247, the 4-ary pulse-amplitude modulation symbol sequence Dm, denoted by 231a, is input to a finite-state machine, denoted by 232b. The blocks of 2 information bits 250 and 251 are also input to 232b. Within 232b, 250 and 251 are input to a subsequence decomposer 237a, which is implemented using an AND gate with inverters on the inputs. The output of 237a is the logical subsequence Sm,0, which is denoted by 238a. The logical subsequence 238a is input to a logical subsequence precoder, which is denoted by 239. The precoder 239 includes the exclusive-OR gate (modulo-2 subtractor), denoted by 240, as well as the one-symbol delay, denoted by 241, interconnected in a feedback arrangement. The output of the logical subsequence precoder 239 is a logical precoded subsequence Zm, denoted by 242a. The logical precoded subsequence 242a is related to the logical subsequence 238a by the rule that, during the mth symbol interval, Zm=Sm,0-Zm-1 (mod2), where Zm-1 (243a) is the value of Zm (242a) during the previous symbol interval, m-1. The precoder 239 is itself a finite-state machine with input Sm,0 (238a), output Zm (242a), and two states, corresponding to the two possible values of Zm-1 (243a), and is described by the state-transition diagram 234, which is shown in
We will now describe the transfer characteristics of typical embodiments of the modulation subsystem 26.
where Vπ is the drive voltage required to cause a phase shift of π. In
where Vπ is the drive voltage required to cause a phase shift of π. In
where Vπ is the drive voltage required to cause a phase shift of π. The drive voltage V3(t) corresponds to 292 in
In order to illustrate the operation of the present invention, we consider the example of a preferred embodiment that uses the encoder 247, which is shown in
The duobinary precoded pulse-amplitude modulation symbol sequence Bm, denoted by 233a, takes on the 2M-1=7 levels indicated in a table 2, below. We assume that in the modulation subsystem 26a, the driver amplifiers 262 and 263 have gains G and -G, respectively, where G=Vπ/6, so that the signal V1(t), denoted by 264, takes on the levels shown in the table 2. We assume that the transmitted optical electric field Etrans(t), denoted by 34a, has a peak value of {square root over (3)}, corresponding to a peak intensity of 3, so that the transmitted optical electric field 34a takes on the levels shown in the table 2. Finally, we assume that the receiver, whether it be 20a, 20b, or 20c, has gain such that the signal v(t), denoted by 43, has a peak value of 3, so that the signal 43 takes on the levels shown in the table 2. In order to simplify this example, we have assumed that the signal v(t) (43) is subject to negligible noise and/or intersymbol interference.
TABLE 2 | ||||
Bm | V1(t) | Etrans(t) | ν(t) | |
-3.00 | -0.50 Vπ | -{square root over (3)} | 3 | |
-1.82 | -0.30 Vπ | -{square root over (2)} | 2 | |
-1.18 | -0.20 Vπ | -1 | 1 | |
0 | 0 | 0 | 0 | |
1.18 | 0.20 Vπ | 1 | 1 | |
1.82 | 0.30 Vπ | {square root over (2)} | 2 | |
3.00 | 0.50 Vπ | {square root over (3)} | 3 | |
We consider another example of a preferred embodiment of the present invention, which uses the encoder 247, which is shown in
We will now discuss three alternate embodiments of duobinary M-ary pulse-amplitude modulation signal encoders of the present invention. In order to explain these three alternate embodiments, it is useful to recall some aspects of the embodiments 229, 229a and 247. Embodiments 229 and 229a are applicable for arbitrary M≧2, whereas embodiment 247 is applicable for M=4, and assumes a specific mapping between pairs of information bits and 4-ary pulse-amplitude modulation symbols. In each of the embodiments 229, 229a and 247, the sequence Dm (denoted by 231, 231 and 231a, respectively, in the three embodiments) is input to the finite-state machine (232, 232a, 232b), which outputs the sequence Bm (233, 233, 233a). The sequence Bm (233, 233, 233a) is related to the sequence Dm (231, 231 and 231a) according to the state-transition diagram 234. The sequence Bm (233, 233, 233a) has the same sign as the sequence Dm (231, 231 and 231a), while the sign of Bm (233, 233, 233a) flips according to 234. In each of the embodiments 229, 229a and 247, the sequence Bm (233, 233, 233a) is lowpass filtered to yield the signal s(t) (236, 236, 236a). Each of the embodiments 229, 229a and 247 can be used with any of the modulation subsystem embodiments 26a, 26b, 26c or 26d. Each of the modulation subsystem embodiments 26a, 26b, 26c, 26d accepts as its input the signal s(t) (236, 236, 236a).
The three alternate encoder embodiments we will now discuss are similar in many respects to embodiments 229, 229a and 247, respectively. The first two of these embodiments (362,
In encoder 362, the sequence 231 is input to a finite-state machine, denoted by 365. In some embodiments of 362, the block of k information bits (23) is also input to the finite-state machine 365, as indicated in
Although in the embodiment 362 we describe the signal 368 as sgn[s(t)] to make clear the relationship between the two encoder embodiments 362 and 229, the signal 368 can take on any two levels that are compatible with the modulation subsystem embodiment (26f,
The encoder 362 can be used with either one of two alternate embodiments of the modulation subsystem (26f,
In describing encoder 362, we have assumed that the level D(0) is nominally zero, and that the remaining M-1 levels, D(1), . . . , D(M-1), are nonzero and all positive. If we were to assume that the levels D(1), . . . , D(M-1), are nonzero and all negative, the encoder 362 would function in an identical manner, except that 364 would represent -|s(t)| and 368 would represent -sgn[s(t)].
In the encoder 362a, the sequence 231 enters the finite-state machine 365a, within which 231 is input to the subsequence decomposer 237, which forms the logical subsequence Sm,0, denoted by 238. The subsequence 238 is a binary sequence having symbol interval T, and is associated with the level D(0). During each symbol interval, the logical subsequence 238 takes on a logical 0 unless the sequence 231 takes on the level D(0), in which case, the logical subsequence 238 takes on a logical 1. Mathematically, during the mth symbol interval, Sm,0=0 if Dm≠D(0) and Sm,0=1 if Dm=D(0).
The logical subsequence 238 is received by the logical subsequence precoder 239. The precoder 239 includes the exclusive-OR gate (modulo-2 subtractor), denoted by 240, as well as the one-symbol delay, denoted by 241, interconnected in a feedback arrangement. The output of the logical subsequence precoder 239 is the logical precoded subsequence Zm, denoted by 242. The logical precoded subsequence 242 is related to the logical subsequence 238 by the rule that, during the mth symbol interval, Zm=Sm,0-Zm-1 (mod2), where Zm-1 (243) is the value of the logical precoded subsequence Zm (242) during the previous symbol interval, m-1. We note that the precoder 239 is itself a finite-state machine with input Sm,0 (238), output Zm (242), and two states, corresponding to the two possible values of Zm-1 (243). The operation of 239 is described by the state-transition diagram 234, shown in
In the encoder 362a, the logical precoded subsequence 242 is input to a level shifter, which is labeled "L/S" and denoted by 369. The level shifter 369 converts a logical input signal (taking on levels corresponding to logical 0 or logical 1, respectively) to a bipolar input signal (taking on equal and opposite levels, e.g., -1 or 1, respectively). In a practical embodiment of the invention, a level shifter 369 may simply correspond to an a.c.-coupling device, e.g., coupling capacitor. The output of the level shifter 369 is the bipolar precoded subsequence sm, denoted by 366. The bipolar precoded subsequence 366 is related to the logical precoded subsequence 242 according to the rule that, during the mth symbol interval, sm=1 if Zm=1 and sm=-1 if Zm=0. Note that, although the sequence Bm (233) is not formed in the encoder embodiment 362a, the sequence sm (366) is a representation of the sign of Bm (233) in the state-transition diagram 234, i.e., sm=1 when Bm>0 and sm=-1 when Bm<0. Note that the sign of Bm is arbitrary when Bm=0. In encoder 362a, the sequence sm (366) passes into a lowpass filter 367, whose output is sgn[s(t)] (368), which is a two-level signal representative of the sign of the duobinary precoded pulse-amplitude modulation signal s(t) (236,
In the embodiment 362a, we have included a level shifter 369 that outputs two equal and opposite levels, to allow us to describe the sequence 366 as sgn[Bm] and to describe the signal 368 as sgn[s(t)]. In a practical implementation of 362a, it may be possible for 369 to output two levels that are not equal and opposite, or it may be possible to omit 369 altogether, so long as the signal 368 takes on two levels that are compatible with the modulation subsystem embodiment (26f,
The encoder 362a can be used with either one of two alternate embodiments of the modulation subsystem (26f,
In describing encoder 362a, we have assumed that the level D(0) is nominally zero, and that the remaining M-1 levels, D(1), ., D(M-1), are nonzero and all positive. If we were to assume that the levels D(1), . . , D(M-1), are nonzero and all negative, the encoder 362 would function in an identical manner, except that 364 would represent -|s(t)| and 368 would represent -sgn[s(t)].
We now provide an example of the alternate embodiment 362 of a duobinary M-ary pulse-amplitude modulation signal encoder for the specific case of M=4, assuming a specific mapping between information bits and 4-ary pulse-amplitude modulation symbols.
In encoder 371, information bits 21 to be transmitted, if in serial form, are passed to the serial-to-parallel converter 22, which forms parallel blocks of 2 bits X1 and X2, denoted by 250 and 251, respectively. Alternatively, if information bits are already in the form of parallel blocks of 2 bits, the serial-to-parallel converter 22 may be omitted. Blocks of 2 information bits 250 and 251 are input to the pulse-amplitude modulation signal encoder 24, which corresponds to 24 in FIG. 2. Within 24, the blocks of 2 information bits 250 and 251 enter the 4-ary pulse-amplitude modulation symbol encoder 230a, which encodes each block of 2 information bits into the 4-ary pulse-amplitude modulation symbol sequence Dm, denoted by 231a. The encoding implemented by 230a is specified in a table 3, below. For our present purposes, we observe that D(0)=0 and that D(0)<D(1)<D(2)<D3, so that this encoding implements Gray coding. Recall that the logical subsequence Sm,0 takes on a logical 1 when Dm=D(0), and takes on a logical 0 otherwise. As indicated in the table 3, for the particular encoding implemented by 230a, 238a takes on the values Sm,0=1 when (X1, X2)=(0,0) and Sm,0=0 otherwise.
TABLE 3 | ||||
X1 | X2 | Dm | Sm,0 | |
0 | 0 | D(0) = 0.00 | 1 | |
0 | 1 | D(1) = 1.18 | 0 | |
1 | 1 | D(2) = 1.82 | 0 | |
1 | 0 | D(3) = 3.00 | 0 | |
The sequence 231a passes into the lowpass filter 363, whose output is |s(t)| (364a), which is the magnitude of the duobinary precoded pulse-amplitude modulation signal s(t). Since the lowpass filter 363 is a linear system, the levels taken on by the signal 364a are proportional to the levels taken on by the sequence 231a. Accordingly, the signal 364a takes on a set of 4 non-negative levels that are proportional to the levels D(0), . . . ., D(3).
In encoder 371, the blocks of 2 information bits 250 and 251 are also input to the subsequence decomposer 237a, which is implemented using an AND gate with inverters on the inputs. The output of 237a is the logical subsequence Sm,0, which is denoted by 238a.
The logical subsequence 238a is input to a logical subsequence precoder, which is denoted by 239. The precoder 239 includes the exclusive-OR gate (modulo-2 subtractor), denoted by 240, as well as the one-symbol delay, denoted by 241, interconnected in a feedback arrangement. The output of the logical subsequence precoder 239 is the logical precoded subsequence Zm, denoted by 242a. The logical precoded subsequence 242a is related to the logical subsequence 238a by the rule that, during the mth symbol interval, Zm=Sm,0-Zm-1 (mod2), where Zm-1 (243a) is the value of the logical precoded subsequence Zm (242a) during the previous symbol interval, m-1. We note that the precoder 239 is itself a finite-state machine with input Sm,0 (238a), output Zm (242a), and two states, corresponding to the two possible values of Zm-l (243a). The operation of 239 is described by the state-transition diagram 234, shown in
In the encoder 371, the logical precoded subsequence 242a is input to the level shifter, which is labeled "L/S" and denoted by 369. The level shifter 369 converts a logical input signal (taking on levels corresponding to logical 0 or logical 1, respectively) to a bipolar input signal (taking on equal and opposite levels, e.g., -1 or 1, respectively). In a practical embodiment of the invention, a level shifter 369 may simply correspond to an a.c.-coupling device, e.g., coupling capacitor. The output of the level shifter 369 is the bipolar precoded subsequence sm, denoted by 366a. The bipolar precoded subsequence 366a is related to the logical precoded subsequence 242a according to the rule that, during the mth symbol interval, sm=1 if Zm=1 and sm=-1 if Zm=0. Note that, although the sequence Bm (233a,
The sequence 366a passes into a lowpass filter 367, whose output is sgn[s(t)] (368a), which is a two-level signal representative of the sign of the duobinary precoded pulse-amplitude modulation signal s(t) (236a,
In the embodiment 371, we have included the level shifter 369 that outputs two equal and opposite levels, to allow us to describe the sequence 366a as sgn[Bm] and to describe the signal 368a as sgn[s(t)]. In a practical implementation of 371, it may be possible for 369 to output two levels that are not equal and opposite, or it may be possible to omit 369 altogether, so long as the signal 368 takes on two levels that are compatible with the modulation subsystem embodiment (26f,
The encoder 371 can be used with either one of two alternate embodiments of the modulation subsystem 26 shown in FIG. 2. These two alternate embodiments (26f,
In describing encoder 371, we have assumed that the level D(0) is nominally zero, and that the remaining 3 levels, D(1), . . . , D(3), are nonzero and all positive. If we were to assume that the levels D(1), . . . , D(3), are nonzero and all negative, the encoder 371 would function in an identical manner, except that 364a would represent -|s(t)| and 368a would represent -sgn[s(t)].
We will now describe two alternate embodiments of the modulation subsystem 26, either of which can be used in conjunction with encoders 362, 362a or 371. These two alternate modulation subsystem embodiments are very similar to 26c and 26d, which are shown in
Considering the general case M≧2, a transmitter that combines encoder 362 or 362a and either of the modulation subsystems 26f or 26g can generate duobinary M-ary pulse-amplitude-modulated optical signals (in the form of the transmitted optical electric field 34f or 34g, respectively) that are equivalent to 34a (generated by encoder 229 or 229a combined with modulation subsystem 26a), 34b (generated by encoder 229 or 229a combined with modulation subsystem 26b), 34c (generated by encoder 229 or 229a combined with modulation subsystem 26c), or 34d (generated by encoder 229 or 229a combined with modulation subsystem 26d). Considering the case M=4 with a particular mapping between information bits and 4-ary pulse-amplitude modulation symbols, a transmitter that combines the encoder 371 and either of the modulation subsystems 26f or 26g can generate duobinary 4-ary pulse-amplitude-modulated optical signals (in the form of the transmitted optical electric field 34f or 34g, respectively) that are equivalent to 34a (generated by encoder 247 combined with modulation subsystem 26a), 34b (generated by encoder 247 combined with modulation subsystem 26b), 34c (generated by encoder 247 combined with modulation subsystem 26c), or 34d (generated by encoder 247 combined with modulation subsystem 26d). In particular, in both the general case M≧2 and the specific case M=4, the transmitted optical electric field 34f or 34g exhibits all of the benefits of a narrowed optical spectrum and lengthened symbol interval that are exhibited by 34a, 34b, 34c and 34d. Also, after transmission through the optical transmission medium 19, the transmitted optical electric field 34f or 34g can be received by any of the three receiver embodiments 20a, 20b, or 20c, like 34a, 34b, 34c and 34d.
The present invention enables information bits to be transmitted via optical signals having a narrowed optical spectrum and lengthened symbol interval, yielding numerous benefits in practical communication systems.
In the present invention, the optical spectrum of the transmitted optical electric field 34 (or 34a-34d and 34f, 34g) depends on several factors, including the information bit rate, the number of levels in the transmitted optical electric field (2M-1), the precise choice of those levels, and the choice of encoder (229, 247, 362 or 371), the design of the lowpass filter(s) (235 or 363 and 367), and the choice of modulation subsystem (26a, 26b, 26c, 26d, 26f or 26g). Nonetheless, for a given information bit rate, for all of the embodiments of duobinary M-ary pulse-amplitude modulation under the present invention, the optical spectrum is narrowed by a factor of approximately 2 as compared to M-ary pulse-amplitude modulation, by a factor of approximately log2M as compared to duobinary 2-ary pulse-amplitude modulation, and by a factor of approximately 2log2M as compared to 2-ary pulse-amplitude modulation (on-off keying).
In order to illustrate the spectral narrowing achieved by the present invention,
The narrowed spectrum illustrated by 414 yields several advantages in practice. In wavelength-division-multiplexed systems, which utilize some form of optical or electrical filters to select the desired signal at the receiver, the spacing between carrier frequencies can be reduced subject to some constraints on the tolerable distortion to the desired signal caused by these filters and the tolerable crosstalk from undesired signals not rejected by these filters, thereby increasing the spectral efficiency of the system. Also, the narrowed optical spectrum reduces pulse spreading caused by chromatic dispersion in systems using single-mode fiber as the transmission medium.
The transmitted optical electric field 34 (or 34a-34d and 34f, 34g) can be described as a duobinary M-ary pulse-amplitude-modulated optical signal, which can be described in terms of a sequence of encoded symbols, each having interval T. In the present invention, the symbol interval T is longer than the symbol interval in systems using 2-ary pulse-amplitude modulation (on-off keying) or duobinary 2-ary pulse-amplitude modulation by a factor log2M, assuming M=2k. For example, when M=4, the symbol interval is lengthened by a factor of 2.
This lengthened symbol interval yields several advantages in practice. The lengthened symbol interval improves a receiver's ability to recover the transmitted information bits in the presence of dispersion (i.e., pulse spreading) originating from several sources, including chromatic dispersion or polarization-mode dispersion in single-mode fiber, modal dispersion in multi-mode fiber, and multipath propagation in free-space links. The lengthened symbol interval also reduces the electrical bandwidth required of electrical-to-optical converters, optical-to-electrical converters and electrical components in the transmitter and receiver. Finally, the lengthened symbol interval reduces the clock speed required in the transmitter and receiver.
In practice, it may be attractive to implement optical communication systems using duobinary 4-ary pulse-amplitude modulation following the present invention. It is of interest to compare such systems to those using 2-ary pulse-amplitude modulation (on-off keying) with non-return-to-zero pulses, which is a modulation technique very widely employed in practice. The use of duobinary 4-ary pulse-amplitude modulation narrows the optical spectrum by approximately a factor of 4, and lengthens the symbol interval by a factor of 2. In dense wavelength-division-multiplexed systems, for a fixed per-channel information bit rate, the narrowed optical spectrum allows the spacing between carrier wavelengths to be reduced by approximately a factor of four, increasing the spectral efficiency of the system by approximately a factor of four.
In a system using single-mode fiber as the transmission medium, the narrowed spectrum and lengthened symbol interval approximately doubles the uncompensated chromatic dispersion that can be tolerated by the system. For example, in a system not using optical compensation of chromatic dispersion, this can permit a doubling of the chromatic-dispersion-limited transmission distance. Alternatively, if optical dispersion compensation is employed, with duobinary 4-ary pulse-amplitude modulation following the present invention, the fiber chromatic dispersion need not be compensated as accurately as it would need to be in a system using 2-ary pulse-amplitude modulation. Also, the lengthened symbol interval doubles the uncompensated polarization-mode dispersion that can be tolerated by the system; if the system does not use optical compensation of polarization-mode dispersion, this permits a quadrupling of the polarization-mode-dispersion-limited transmission distance.
Additionally, the lengthened symbol interval cuts approximately in half the electrical bandwidth required of electrical-to-optical converters, optical-to-electrical converters and electrical components in the transmitter and receiver. Finally, the lengthened symbol interval reduces the clock speed required in the transmitter and receiver by a factor of two.
Although the present invention has been described in terms of the presently preferred embodiments, it is to be understood that such disclosure is not to be interpreted as limiting. Various alterations and modifications will no doubt become apparent to those skilled in the art after having read the above disclosure. Accordingly, it is intended that the appended claims be interpreted as covering all alterations and modifications as fall within the true spirit and scope of the invention.
Kahn, Joseph Mardell, Ho, Keangpo
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